Inviscid Shallow-Water Theory
- 896 Downloads
In this chapter we take up the study of the dynamics of a shallow, rotating layer of homogeneous incompressible and inviscid fluid. There are two purposes to our consideration of this physical system. It is first of all simple enough so that the issues raised by the problem of geostrophic degeneracy can be dealt with directly without the need to simultaneously treat the complexities of the thermodynamics of a density-stratified fluid. The first goal of the present chapter is to illustrate how the geostrophic approximation can be systematically exploited to produce a deterministic dynamical framework adequate for the calculation of motions of large time and space scales. Furthermore, the method of analysis to be presented also can be generalized to the study of thermodynamically active fluids. The key technique of the analysis is the formulation of a systematic approximation scheme in which the geostrophic approximation is merely the first step.
KeywordsWave Packet Group Velocity Rossby Wave Potential Vorticity Phase Speed
Unable to display preview. Download preview PDF.
- Rossby, C. G., et al. 1939. Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action. J. Marine Res. 2, 38–55.Google Scholar
- Stommel. H. 1948. The westward intensification of wind-driven ocean currents. Trans. Amer. Geoph. Union 29, 202–206.Google Scholar
- Longuet-Higgins, M. S. 1964. On group velocity and energy flux in planetary wave motions. Deep-Sea Research 11, 35–42.Google Scholar
- Jeffreys, H. A. and Jeffreys, B. S. 1962. Methods of Mathematical Physics Cambridge University Press.Google Scholar
- Greenspan, H. P. 1968. The Theory of Rotating Fluids. Cambridge University Press, 327 pp.Google Scholar
- Batchelor, G. K. 1953. Theory of Homogeneous Turbulence. Cambridge University Press, 197 pp.Google Scholar
- Batchelor, G. K. 1969. Computation of the energy spectrum in homogeneous two-dimensional turbulence. The Physics of Fluids, Supplement II, pp. 233–239.Google Scholar
- Rhines, P. B. 1977. The dynamics of unsteady ocean currents. In The Sea, Vol. VI, Wiley, pp. 189–318.Google Scholar